Title: Violation of unitarity by Hawking radiation does not violate energy-momentum conservation

Abstract

An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.

Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 04; Other Information: PUBLISHER-ID: JCAP04(2015)002; OAI: oai:repo.scoap3.org:9836; Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

@article{osti_22454535,
title = {Violation of unitarity by Hawking radiation does not violate energy-momentum conservation},
author = {Nikolić, Hrvoje},
abstractNote = {An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.},
doi = {10.1088/1475-7516/2015/04/002},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 04,
volume = 2015,
place = {United States},
year = {Thu Apr 02 00:00:00 EDT 2015},
month = {Thu Apr 02 00:00:00 EDT 2015}
}

An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentummore » is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.« less

Black hole greybody factors carry some quantum black hole information. Studying greybody factors may lead to understanding the quantum nature of black holes. However, solving for exact greybody factors in many black hole systems is impossible. One way to deal with this problem is to place some rigorous analytic bounds on the greybody factors. In this paper, we calculate rigorous bounds on the greybody factors for spin zero hawking radiation for non-zero-angular momentum mode from the Kerr-Newman black holes.

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux. -- Highlights:more » •A cosmic string is introduced along the axis of symmetry of the dyonic black hole. •The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed. •Both angular and radial parts are transformed to a confluent Heun equation. •The resulting Hawking radiation spectrum and the energy flux are obtained.« less

Purpose: To determine independent predictors of lymphedema (LE) after breast radiotherapy and to quantify added risks of LE from regional node irradiation (RNI). Materials and Methods: A total of 2,579 women with T1-2, N 0-3, M0 breast cancer treated with breast conservation between 1970 and 2005 were studied. A total of 2,169 patients (84%) received radiation to the breast (B), 226 (8.8%) to the breast and supraclavicular LNs (B+SC), and 184 (7.1%) to the breast, supraclavicular LNs, and a posterior axillary boost (B+SC+PAB). Median follow-up was 81 months (range, 3-271). Results: Eighteen percent of patients developed LE. LE risks weremore » as follows: 16% (B), 23% (B+SC), and 31% (B+SC+PAB) (p < 0.0001). LE severity was greater in patients who had RNI (p = 0.0002). On multivariate analysis, RT field (p < 0.0001), obesity index (p = 0.0157), systemic therapy (p = 0.0013), and number of LNs dissected (p < 0.0001) independently predicted for LE. In N1 patients, the addition of a SC to tangents (p < 0.0001) and the addition of a PAB to tangents (p = 0.0017) conferred greater risks of LE, but adding a PAB to B+SC RT did not (p = 0.8002). In the N2 patients, adding a PAB increased the risk of LE 4.5-fold over B+SC RT (p = 0.0011). Conclusions: LE predictors included number of LNs dissected, RNI, obesity index, and systemic therapy. LE risk increased when a SC or PAB were added in the N1 subgroup. In the N2 patients, a PAB increased the risk over B+SC. The decision to boost the axilla must be weighed against the increased risk of LE that it imposes.« less

The connection between QCD, a nonlocal Nambu-Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson-Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, {Gamma}{sub {pi}{yields}{gamma}{gamma}} and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson-Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of themore » above scenarios. Furthermore, the nonlocal Nambu-Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.« less